The document provides various multiplication shortcuts and methods for multiplying multi-digit numbers. It includes steps for multiplying 2-digit and 3-digit numbers, as well as shortcuts and patterns for multiplying numbers ending or beginning with certain digits by 9, 12, or 6. Divisibility rules for 7 and methods for finding percentages and converting fractions to percentages are also summarized.

1. Multiplication Shortcuts

2. Multiplication of 2 digit with 2 digit
• 67 × 56
• Step 1: 7 × 6 = 42
• Step 2: (6×6) + (5×7) =
71 +4(carry) = 75
• Step 3: 6 × 5 = 30 +
7(carry) = 37

3. Multiplication of 3 digit with 3 digit
• 789 × 123
• Step 1: 3 × 9 = 27
• Step 2: (8×3) + (9×2) = 42
+ 2(Carry) = 44
• Step 3: (7 × 3) + (1 × 9) +
(8 × 2) = 46 + 4(Carry) =
50
• Step 4: (7 × 2) + (8 × 1) =
22 + 5(Carry) = 27
• Step 5: 7 × 1 = 7 +
2(Carry) =9

4. Divisibility by 7

5. Find % ending in 0 or 5

6. To find the % of any Number

7. Convert Fractions into %

8. Multiply the Big Numbers

9. Squaring a number ending in 5
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352 =?
The successor of 3 is 4
Multiply 3 and 4
Put the answer 12.
Suffix 25.
The answer is 1225.

10. Squaring the number beginning in 5
• 562 = ?
• Always Add 25 with the
number in units digit
25+6 = 31
• Suffix the square of the
unit digit = 36

11. Squaring a number beginning in 1
1
18 6
196
142 = ?
42 = 16
Put 6. Carry one
14 + 4 = 18
Add 18 and carry and put the answer in front

13. Multiplication by 9
• For 1 to 9
• Subtract 1.
• Annex the 9’s complement.
7 x 9 = 63
• For 11 to 19
• Subtract 2.
• Annex the 9’s complement.
17 x 9 = 153
• For 21 to 29
• Subtract 3.
• Annex the 9’s complement.
26 x 9 = 234

14. Numbers ending in 6
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662 =_________.
a) Write down 6.
b) 2 x (6 + 1) + 1 = 15. Write 5, carry *1.
c) 6 x (6 + 1) = 42 + *1 = 43. Write 43.
d) The answer is 4356.
862 =_________.
a) Write down 6.
b) 2 x (8 + 1) + 1 = 19. Write 9, carry *1.
c) 8 x (8 + 1) = 72 + *1 = 73. Write 73.
d) The answer is 7396.

15. Multiplication by 12
• Let’s understand this method by
taking an example.
• 345 × 12
• Step 1:
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Write 345 as 0345.
• Step 2:
• Multiply each and every digit with
2 and add it to its right neighbour.
This process is started from right.
Multiply 5 with 2 and add it to its
right neighbour. 5 has no right
neighbour so add the
multiplication to 0. This gives 10
as a result. So 0 is written down
and 1 is carried forward.

16. • Step 3:
• Multiply 4 with 2 and add it to 5.
Carry 1 is added to the result. This
gives 14 as a result.
• 4 is written down and 1 is carry
forwarded.

17. • Step 4:
• Multiply 3 with 2 and add it
to 4. Carry 1 is added to the
result. This gives 11 as a
result.
• 1 is written down and 1 is
carry forwarded.

18. • Step 5:
• Multiply 0 with 2 and add it
to 3. Carry 1 is added to the
result. This gives 4 as a
result.

19. MULTIPLICATION BY SIX
Practice what is half of ?
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6
5
4
8
7
2
To each number add ‘half’ of the neighbour;
‘plus 5’ if it is odd
1
• 3 0 6 2 2 0 8 4x6
• 2 3 7 3 2 5 0 4
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2
4
3
1
1
0 4 4 3 0 5 2x6
2 6 5 8 3 1 2